"""The paper (ltl.tex, §5.3, App. B) claims the *recursive* inclusion and
consistency verifiers it defines and proves about are equivalent to the
deployed iterative RFC 9162 verifiers, and cites exhaustive
differential-testing counts. This test IS that verification, so the paper's
numbers cannot silently rot: it reproduces the exact recursive forms
written in the paper and asserts full agreement with the deployed code over
all sizes up to 256, honest inputs plus adversarial mutations, and pins the
cited case counts (164,479 inclusion; 164,224 consistency).
"""

import hashlib

from pacta.transparency import (
    consistency_proof,
    inclusion_proof,
    merkle_root,
    verify_consistency,
    verify_inclusion,
)

NMAX = 256


def _h(b: bytes) -> bytes:
    return hashlib.sha256(b).digest()


def _hleaf(d: bytes) -> bytes:
    return _h(b"\x00" + d)


def _hnode(x: bytes, y: bytes) -> bytes:
    return _h(b"\x01" + x + y)


def _k_below(n: int) -> int:
    k = 1
    while 2 * k < n:
        k *= 2
    return k


# --- the paper's recursive inclusion verifier (App. B) ---------------------
def _root(v, m, n, path):
    if n == 1:
        if path:
            raise ValueError
        return v
    if not path:
        raise ValueError
    *rest, s = path
    k = _k_below(n)
    return _hnode(_root(v, m, k, rest), s) if m < k else _hnode(s, _root(v, m - k, n - k, rest))


def _paper_incl(d, m, n, path, root):
    if not (0 <= m < n):
        return False
    try:
        return _root(_hleaf(d), m, n, path) == root
    except ValueError:
        return False


# --- the paper's recursive consistency verifier (§5.3, ConsRec) ------------
def _consrec(m, n, P, b, r0):
    if m == n:
        if b:
            if P:
                raise ValueError
            return (r0, r0)
        if len(P) != 1:
            raise ValueError
        return (P[0], P[0])
    if not P:
        raise ValueError
    *rest, s = P
    k = _k_below(n)
    if m <= k:
        x, y = _consrec(m, k, rest, b, r0)
        return (x, _hnode(y, s))
    xr, yr = _consrec(m - k, n - k, rest, False, r0)
    return (_hnode(s, xr), _hnode(s, yr))


def _paper_cons(m, n, r0, r1, P):
    if m == 0:
        return True
    if m > n:
        return False
    try:
        x, y = _consrec(m, n, P, True, r0)
    except ValueError:
        return False
    return x == r0 and y == r1


def test_recursive_inclusion_equals_deployed_exhaustive():
    total = 0
    for n in range(1, NMAX + 1):
        data = [bytes([i % 251]) + bytes([(i * 5) % 256]) * (i % 3) for i in range(n)]
        root = merkle_root(data)
        for m in range(n):
            P = inclusion_proof(data, m)
            cases = [
                (data[m], m, n, P, root),
                (data[m] + b"!", m, n, P, root),
                (data[m], (m + 1) % n, n, P, root),
                (data[m], m, n, P, _h(b"q")),
            ]
            if P:
                cases.append((data[m], m, n, P[:-1], root))
            for d2, m2, n2, P2, r2 in cases:
                total += 1
                assert verify_inclusion(d2, m2, n2, P2, r2) == _paper_incl(d2, m2, n2, P2, r2), (n, m)
            assert verify_inclusion(data[m], m, n, P, root)
            assert _paper_incl(data[m], m, n, P, root)
    assert total == 164_479, total  # the count cited in the paper


def test_recursive_consistency_equals_deployed_exhaustive():
    total = 0
    for n in range(1, NMAX + 1):
        data = [bytes([i % 251]) + bytes([(i * 7) % 256]) * (i % 4) for i in range(n)]
        r1 = merkle_root(data)
        for m in range(1, n + 1):
            P = consistency_proof(data, m)
            r0 = merkle_root(data[:m])
            cases = [
                (m, n, r0, r1, P),
                (m, n, _h(b"x"), r1, P),
                (m, n, r0, _h(b"y"), P),
                (m, n, r0, r1, P + [_h(b"z")]),
            ]
            if P:
                cases.append((m, n, r0, r1, P[:-1]))
            for mm, nn, a, bb, pp in cases:
                total += 1
                assert verify_consistency(mm, nn, a, bb, pp) == _paper_cons(mm, nn, a, bb, pp), (n, m)
            assert verify_consistency(m, n, r0, r1, P)
            assert _paper_cons(m, n, r0, r1, P)
    assert total == 164_224, total  # the count cited in the paper